*4.1. Fuzzification*

The crisp values of the two inputs are mapped into fuzzy sets using the triangle membership function. Both inputs are defined using five fuzzy sets as shown in Figures 3 and 4. The sets of the inputs are defined as: very large (VL), large (L), medium (m), small (S), and very small (VS).

**Figure 3.** Membership function (changing in grid's frequency).

**Figure 4.** Membership function (power reserve).

The absolute value of the rate of change in the grid's frequency is represented by the first membership (Figure 3), whereas the available reserved power is represented by the second membership function (Figure 4). In this paper, frequency drop less than 0.2 Hz is defined by the fuzzy sets as very small (VS) and above 0.8 Hz is defined as very large (VL).

In this article, wind energy systems rated at 2 MW are considered. In these wind energy systems, the amount of reserve can range from 100 kW to 1 MW (i.e., 5% to 50% of the maximum power). For simplification, the power reserve is measured and scaled down before it enters the membership function. The dynamic rate is given by the output membership function shown in Figure 5. The output is determined by the following fuzzy sets: very fast (VF), fast (F), medium (M), slow (SL) and very slow (VSL). This output is then used to determine the rate of change in injected active power given in (3). The rules of the fuzzy logic used to define the output are discussed in the following section.

**Figure 5.** Membership function (output).
